Development of an optimal state transition graph for trajectory optimisation of dynamic systems by application of Dijkstra's algorithm

Abstract

A technique is presented for modelling a dynamic system defined by differential-algebraic equations into a weighted directed graph of optimal state transitions. This aims to make it possible for the fixed final state optimal control problem of a dynamic system to be solved through shortest path graph search. The graph is generated by taking a defined dynamic system state space and modelling discrete states as vertices and the transitions between states as edges. The edge weights are optimized to represent the optimal transitions between their connected state-vertices, resulting in an optimal state transition graph. An optimal control solution for an optimal control problem can be determined by applying Dijkstra’s algorithm to this optimized graph. The graph is generated to have n-connections between the system states instead of n2-connections, allowing for a shortest path from an initial state to a specified final state to be determined at a feasible computational run-time.